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Chebyshev and Fourier Spectral Methods: Second Revised Edition (Dover Books on Mathematics) - Paperback
2001, ISBN: 0486411834
ID: 14067798390
[EAN: 9780486411835], [PU: Dover Publications], Mathematics|Functional Analysis, Mathematics|General, Science|Mathematical Physics, This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed. Summary: Preface; Acknowledgments; Errata and Extended-Bibliography 1. Introduction 1.1 Series expansions 1.2 First example 1.3 Comparison with finite element methods 1.4 Comparisons with finite differences 1.5 Parallel computers 1.6 Choice of basis functions 1.7 Boundary conditions 1.8 Non-Interpolating and Pseudospectral 1.9 Nonlinearity 1.10 Time-dependent problems 1.11 FAQ: frequently asked questions 1.12 The chrysalis 2. Chebyshev & Fourier series 2.1 Introduction 2.2 Fourier series 2.3 Orders of convergence 2.4 Convergence order 2.5 Assumption of equal errors 2.6 Darboux's principle 2.7 Why Taylor series fail 2.8 Location of singularities 2.8.1 Corner singularities & compatibility conditions 2.9 FACE: Integration-by-Parts bound 2.10 Asymptotic calculation of Fourier coefficients 2.11 Convergence theory: Chebyshev polynomials 2.12 Last coefficient rule-of-thumb 2.13 Convergence theory for Legendre polynomials 2.14 Quasi-Sinusoidal rule of thumb 2.15 Witch of Agensi rule-of-thumb 2.16 Boundary layer rule-of-thumb 3. Galerkin & Weighted residual methods 3.1 Mean weighted residual methods 3.2 Completeness and boundary conditions 3.3 Inner product & orthogonality 3.4 Galerkin method 3.5 Integration-by-Parts 3.6 Galerkin method: case studies 3.7 Separation-of-Variables & the Galerkin method 3.8 Heisenberg Matrix mechanics 3.9 The Galerkin method today 4. Interpolation, collocation & all that 4.1 Introduction 4.2 Polynomial interpolation 4.3 Gaussian integration & pseudospectral grids 4.4 Pseudospectral Is Galerkin method via Quadrature 4.5 Pseudospectral errors 5. Cardinal functions 5.1 Introduction 5.2 Whittaker cardinal or "sinc" functions 5.3 Trigonometric interpolation 5.4 Cardinal functions for orthogonal polynomials 5.5 Transformations and interpolation 6. Pseudospectral methods for BVPs 6.1 Introduction 6.2 Choice of basis set 6.3 Boundary conditions: behavioral & numerical 6.4 "Boundary-bordering" 6.5 "Basis Recombination" 6.6 Transfinite interpolation 6.7 The Cardinal function basis 6.8 The interpolation grid 6.9 Computing basis functions & derivatives 6.10 Higher dimensions: indexing 6.11 Higher dimensions 6.12 Corner singularities 6.13 Matrix methods 6.14 Checking 6.15 Summary 7. Linear eigenvalue problems 7.1 The No-brain method 7.2 QR/QZ Algorithm 7.3 Eigenvalue rule-of-thumb 7.4 Four kinds of Sturm-Liouville problems 7.5 Criteria for Rejecting eigenvalues 7.6 "Spurious" eigenvalues 7.7 Reducing the condition number 7.8 The power method 7.9 Inverse power method 7.10 Combining global & local methods 7.11 Detouring into the complex plane 7.12 Common errors 8. Symmetry & parity 8.1 Introduction 8.2 Parity 8.3 Modifying the Grid to Exploit parity 8.4 Other discrete symmetries 8.5 Axisymmetric & apple-slicing models 9. Explicit time-integration methods 9.1 Introduction 9.2 Spatially-varying coefficients 9.3 The Shamrock principle 9.4 Linear and nonlinear 9.5 Example: KdV equation 9.6 Implicitly-Implicit: RLW & QG 10. Partial summation, the FFT and MMT 10.1 Introduction 10.2 Partial summation 10.3 The fast Fourier transform: theory 10.4 Matrix multiplication transform 10.5 Costs of the fast Fourier transform 10.6 Generalized FFTs and multipole methods 10.7 Off-grid interpolation 10.8 Fast Fourier transform: practical matters 10.9 Summary 11. Aliasing, spectral blocking, & blow-up 11.1 Introduction 11.2 Aliasing and Equality-on-the-grid 11.3 "2 h-Waves" and spectral blocking 11.4 Aliasing instability: history and remedies 11.5 Dealiasing
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John P. Boyd:
Chebyshev and Fourier Spectral Methods: Second Revised Edition (Dover Books on Mathematics) - Paperback2001, ISBN: 0486411834
ID: 14068320655
[EAN: 9780486411835], Neubuch, [PU: Dover Publications], Mathematics|Functional Analysis, Mathematics|General, Science|Mathematical Physics, Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface; Acknowledgments; Errata and Extended-Bibliography 1. Introduction 1.1 Series expansions 1.2 First example 1.3 Comparison with finite element methods 1.4 Comparisons with finite differences 1.5 Parallel computers 1.6 Choice of basis functions 1.7 Boundary conditions 1.8 Non-Interpolating and Pseudospectral 1.9 Nonlinearity 1.10 Time-dependent problems 1.11 FAQ: frequently asked questions 1.12 The chrysalis 2. Chebyshev & Fourier series 2.1 Introduction 2.2 Fourier series 2.3 Orders of convergence 2.4 Convergence order 2.5 Assumption of equal errors 2.6 Darboux's principle 2.7 Why Taylor series fail 2.8 Location of singularities 2.8.1 Corner singularities & compatibility conditions 2.9 FACE: Integration-by-Parts bound 2.10 Asymptotic calculation of Fourier coefficients 2.11 Convergence theory: Chebyshev polynomials 2.12 Last coefficient rule-of-thumb 2.13 Convergence theory for Legendre polynomials 2.14 Quasi-Sinusoidal rule of thumb 2.15 Witch of Agensi rule-of-thumb 2.16 Boundary layer rule-of-thumb 3. Galerkin & Weighted residual methods 3.1 Mean weighted residual methods 3.2 Completeness and boundary conditions 3.3 Inner product & orthogonality 3.4 Galerkin method 3.5 Integration-by-Parts 3.6 Galerkin method: case studies 3.7 Separation-of-Variables & the Galerkin method 3.8 Heisenberg Matrix mechanics 3.9 The Galerkin method today 4. Interpolation, collocation & all that 4.1 Introduction 4.2 Polynomial interpolation 4.3 Gaussian integration & pseudospectral grids 4.4 Pseudospectral Is Galerkin method via Quadrature 4.5 Pseudospectral errors 5. Cardinal functions 5.1 Introduction 5.2 Whittaker cardinal or "sinc" functions 5.3 Trigonometric interpolation 5.4 Cardinal functions for orthogonal polynomials 5.5 Transformations and interpolation 6. Pseudospectral methods for BVPs 6.1 Introduction 6.2 Choice of basis set 6.3 Boundary conditions: behavioral & numerical 6.4 "Boundary-bordering" 6.5 "Basis Recombination" 6.6 Transfinite interpolation 6.7 The Cardinal function basis 6.8 The interpolation grid 6.9 Computing basis functions & derivatives 6.10 Higher dimensions: indexing 6.11 Higher dimensions 6.12 Corner singularities 6.13 Matrix methods 6.14 Checking 6.15 Summary 7. Linear eigenvalue problems 7.1 The No-brain method 7.2 QR/QZ Algorithm 7.3 Eigenvalue rule-of-thumb 7.4 Four kinds of Sturm-Liouville problems 7.5 Criteria for Rejecting eigenvalues 7.6 "Spurious" eigenvalues 7.7 Reducing the condition number 7.8 The power method 7.9 Inverse power method 7.10 Combining global & local methods 7.11 Detouring into the complex plane 7.12 Common errors 8. Symmetry & parity 8.1 Introduction 8.2 Parity 8.3 Modifying the Grid to Exploit parity 8.4 Other discrete symmetries 8.5 Axisymmetric & apple-slicing models 9. Explicit time-integration methods 9.1 Introduction 9.2 Spatially-varying coefficients 9.3 The Shamrock principle 9.4 Linear and nonlinear 9.5 Example: KdV equation 9.6 Implicitly-Implicit: RLW & QG 10. Partial summation, the FFT and MMT 10.1 Introduction 10.2 Partial summation 10.3 The fast Fourier transform: theory 10.4 Matrix multiplication transform 10.5 Costs of the fast Fourier transform 10.6 Generalized FFTs and multipole methods 10.7 Off-grid interpolation 10.8 Fast Fourier transform: practical matters 10.9 Summary 11. Aliasing, spectral blocking, & blow-up 11.1 Introduction 11.2 Aliasing and Equality-on-the-grid 11.3 "2 h-Waves" and spectral blocking 11.4 Aliasing instability: history and remedies 11.5 Dealiasing
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Chebyshev and Fourier Spectral Methods (Revised)[ CHEBYSHEV AND FOURIER SPECTRAL METHODS (REVISED) ] By Boyd, John Philip ( Author )Dec-03-2001 Paperback - Paperback
2001
ISBN: 0486411834
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2003, ISBN: 9780486411835
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Title: | Chebyshev and Fourier Spectral Methods |
ISBN: | 0486411834 |
Details of the book - Chebyshev and Fourier Spectral Methods
EAN (ISBN-13): 9780486411835
ISBN (ISBN-10): 0486411834
Hardcover
Paperback
Publishing year: 2001
Publisher: DOVER PUBN INC
688 Pages
Weight: 0,907 kg
Language: eng/Englisch
Book in our database since 24.04.2007 19:16:15
Book found last time on 30.01.2017 16:04:36
ISBN/EAN: 0486411834
ISBN - alternate spelling:
0-486-41183-4, 978-0-486-41183-5
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